Cosine of 225 Degrees

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Theorem

$\cos 225 \degrees = \cos \dfrac {5 \pi} 4 = -\dfrac {\sqrt 2} 2$

where $\cos$ denotes cosine.


Proof

\(\ds \cos 225 \degrees\) \(=\) \(\ds \map \cos {360 \degrees - 135 \degrees}\)
\(\ds \) \(=\) \(\ds \cos 135 \degrees\) Cosine of Conjugate Angle
\(\ds \) \(=\) \(\ds -\frac {\sqrt 2} 2\) Cosine of $135 \degrees$

$\blacksquare$


Sources